We consider the focusing nonlinear Schrödinger equation with inverse square poten-Using the profile decomposition obtained recently by the first author [1], we show that in the L 2 -subcritical case, i.e. 0 < α < 4 d , the sets of ground state standing waves are orbitally stable. In the L 2 -critical case, i.e. α = 4 d , we show that ground state standing waves are strongly unstable by blow-up.
In this paper, we prove a refined version of a compactness lemma and we use it to establish mass-concentration for the focusing nonlinear Schrödinger equation with an inverse-square potential.
We investigate the initial value problem for a defocusing nonlinear Schrödinger equation with weighted exponential nonlinearitywhere 0 < b < 1 and α = 2π(2 − b). We establish local and global well-posedness in the subcritical and critical regimes.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.